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A quadratic form with integer coefficients is called an integral binary quadratic form, often abbreviated to binary quadratic form. This article is entirely devoted to integral binary quadratic forms. This choice is motivated by their status as the driving force behind the development of algebraic number theory.
This page contains tables of azeotrope data for various binary and ternary mixtures of solvents. The data include the composition of a mixture by weight (in binary azeotropes, when only one fraction is given, it is the fraction of the second component), the boiling point (b.p.) of a component, the boiling point of a mixture, and the specific gravity of the mixture.
In mathematics, in number theory, Gauss composition law is a rule, invented by Carl Friedrich Gauss, for performing a binary operation on integral binary quadratic forms (IBQFs). Gauss presented this rule in his Disquisitiones Arithmeticae , [ 1 ] a textbook on number theory published in 1801, in Articles 234 - 244.
A mapping q : M → R : v ↦ b(v, v) is the associated quadratic form of b, and B : M × M → R : (u, v) ↦ q(u + v) − q(u) − q(v) is the polar form of q. A quadratic form q : M → R may be characterized in the following equivalent ways: There exists an R-bilinear form b : M × M → R such that q(v) is the associated quadratic form.
Reduction 4H + + 4e − → 2H 2 E° = 0.00 V vs. NHE Overall 2H 2 O → 2H 2 + O 2 E°cell = +1.23 V; ΔG = 475 kJ/mol . Water splitting can be done at higher pH values as well however the standard potentials will vary according to the Nernst equation and therefore shift by -59 mV for each pH unit increase. However, the total cell potential ...
The Margules activity model is a simple thermodynamic model for the excess Gibbs free energy of a liquid mixture introduced in 1895 by Max Margules. [1] [2] After Lewis had introduced the concept of the activity coefficient, the model could be used to derive an expression for the activity coefficients of a compound i in a liquid, a measure for the deviation from ideal solubility, also known as ...
For binary quadratic forms there is a group structure on the set C of equivalence classes of forms with given discriminant. The genera are defined by the generic characters . The principal genus, the genus containing the principal form, is precisely the subgroup C 2 and the genera are the cosets of C 2 : so in this case all genera contain the ...
Pages in category "Quadratic forms" The following 61 pages are in this category, out of 61 total. ... Binary quadratic form; Brauer–Wall group; Büchi's problem; C.